Conventionally, in order to promote an engine warm-up, there is provided with a normal mode purpose gear-shift map and a warm-up promotion purpose gear-shift map. In a case where an engine cooling water (coolant) temperature is a low temperature, a switching to the gear-shift using the warming-up purpose gear-shift map is carried out. It should herein be noted that, since the warm-up promotion purpose gear-shift map has a switching gear-shift line from a low speed stage to a high speed stage which is set to be offset toward a higher vehicle speed side in order to increase an engine rotation speed according to such a tendency as to expand a selection of the low speed stage. In addition, a stepped automatic transmission having a one way clutch which is engaged at the low speed stage in the driving state and which runs idle in a coast state (for example, refer to Patent Document 1).